Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
510 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 510 conjugacy classes of subgroups — too many to draw. Only its 125 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C32×#443 | C2 | semidirect |
| 2. #10592892 | C2 | semidirect |
| 3. #10592394 | C2 | semidirect |
| 4. #10589361 | C2 | semidirect |
| 5. #10589329 | C2 | semidirect |
| 18. C3×#443 | D3 | semidirect |
| 26. C32×Q16 | D4 | semidirect |
| 28. C32×D8 | D4 | semidirect |
| 69. #443 | C3⋊D3 | semidirect |
| 75. C3×Q16 | D12 | semidirect |
| 77. C3×D8 | D12 | semidirect |
| 130. Q16 | C4⋊(C3⋊D3) | semidirect |
| 136. D8 | C4⋊(C3⋊D3) | semidirect |
| 152. C32 | #2213 | semidirect |
| 180. C3 | #70926 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×#443 | 2 |
| #10592892 | 2 |
| #10592394 | 2 |
| #10589361 | 2 |
| #10589329 | 2 |
| #70926 | 3 |